A time-dependent Fourier grid Hamiltonian-based formulation of time-dependent multi-configuration Hartree method

We propose a variant of the time-dependent multi-configuration Hartree method within the framework of Fourier grid Hamiltonian method. The workability of the method proposed is demonstrated with a well-known coupled two-mode problem.     

A new mixed self-consistent field procedure

A new approach for the calculation of three-centre electronic repulsion integrals (ERIs) is developed, implemented and benchmarked in the framework of auxiliary density functional theory (ADFT). The so-called mixed self-consistent field (mixed SCF) divides the computationally costly ERIs in two sets: far-field and near-field. Far-field ERIs are calculated using the newly developed double asymptotic expansion as in the direct SCF scheme. Near-field ERIs are calculated only once prior to the SCF procedure and stored in memory, as in the conventional SCF scheme. Hence the name, mixed SCF. The implementation is particularly powerful when used in parallel architectures, since all RAM available are used for near-field ERI storage. In addition, the efficient distribution algorithm performs minimal intercommunication operations between processors, avoiding a potential bottleneck. One-, two- and three-dimensional systems are used for benchmarking, showing substantial time reduction in the ERI calculation for all of them. A Born–Oppenheimer molecular dynamics calculation for the Na⁺₅₅ cluster is also shown in order to demonstrate the speed-up for small systems achievable with the mixed SCF.     

A self-consistent field theory of crystals

A self-consistent theory of crystals is presented. The classical phenomenological theory of crystals is derived by means of the boson transformation method.     

A partially self-consistent phenomenological nuclear mean field

A version of a partially self-consistent phenomenological mean field of a nucleus that considers the effect of nucleon density polarization due to particle-hole interaction is proposed. Allowing for this effect enables us to fit the calculated charge radius of the nucleus and the energies of isobaric analog resonance to the corresponding observed magnitudes without using any additional parameters.     

A parallel algorithm for solving the 3d Schrödinger equation

We describe a parallel algorithm for solving the time-independent 3d Schrödinger equation using the finite difference time domain (FDTD) method. We introduce an optimized parallelization scheme that reduces communication overhead between computational nodes. We demonstrate that the compute time, t, scales inversely with the number of computational nodes as t ∝ (N_nodes)^{−0.95 ± 0.04}. This makes it possible to solve the 3d Schrödinger equation on extremely large spatial lattices using a small computing cluster. In addition, we present a new method for precisely determining the energy eigenvalues and wavefunctions of quantum states based on a symmetry constraint on the FDTD initial condition. Finally, we discuss the usage of multi-resolution techniques in order to speed up convergence on extremely large lattices.     

基于Hadoop二阶段并行模糊c-Means数据聚类算法

为了解决Mapreduce机制下算法通信时间占用比过高实际应用价值受限的情况,提出基于Hadoop二阶段并行c-Means聚类算法用来解决超大数据的分类问题。首先,改进Mapreduce机制下的MPI通讯管理方法,采用成员管理协议方式实现成员管理与Mapreduce降低操作的同步化。其次,实行典型个体组降低操作代替全局个体降低操作,并定义二阶段缓冲算法,通过第一阶段的缓冲进一步降低第二阶段Mapreduce操作的数据量,尽可能降低大数据带来的对算法负面影响。最后,利用人造大数据测试集进行仿真实验表明此算法既能保证聚类精度要求又可有效加快算法运行效率。     

High-temperature protonic motion and low-temperature lattice deformation in one-dimensional hydrogen-bonded molecular chain in tetramethylpyrazine–chloranilic acid (1:1)

Recent theoretical advances have identified several computational algorithms that can be implemented utilizing quantum information processing (QIP), which gives an exponential speedup over the corresponding (known) algorithms on conventional computers. QIP makes use of the counter-intuitive properties of quantum mechanics, such as entanglement and the superposition principle. Unfortunately it has so far been impossible to build a practical QIP system that outperforms conventional computers. Atomic ions confined in an array of interconnected traps represent a potentially scalable approach to QIP. All basic requirements have been experimentally demonstrated in one and two qubit experiments. The remaining task is to scale the system to many qubits while minimizing and correcting errors in the system. While this requires extremely challenging technological improvements, no fundamental roadblocks are currently foreseen.     

A self-consistent field for the H2 molecule

We investigate the simple harmonic oscillator in a 1D box, and the 2D isotropic harmonic oscillator problem in a circular cavity with perfectly reflecting boundary conditions. The energy spectrum has been calculated as a function of the self-adjoint extension parameter. For sufficiently negative values of the self-adjoint extension parameter, there are bound states localized at the wall of the box or the cavity that resonate with the standard bound states of the simple harmonic oscillator or the isotropic oscillator. A free particle in a circular cavity has been studied for the sake of comparison. This work represents an application of the recent generalization of the Heisenberg uncertainty relation related to the theory of self-adjoint extensions in a finite volume.     

Analysis of multi-configuration density functional theory methods: theory and model application to bond-breaking

We consider the extension of the standard single-determinant Kohn–Sham method to the case of a multi-configuration auxiliary wave function. By applying the rigorous Kohn–Sham method to this case, we construct the proper interacting and auxiliary energy functionals. Following the Hohenberg–Kohn theorem for both energy functionals, we derive the corresponding multi-configuration Kohn–Sham equations, based on a local effective potential. At the end of the analysis we show that, at the ground state, the auxiliary wavefunction must collapse into a single-determinant wave function, equal to the regular KS wavefunction. We also discuss the stability of the wavefunction in multi-configuration density functional theory methods where the auxiliary system is partially interacting, and the remaining (residual) correlation is evaluated as a functional of the density. As an example showing both the challenges and the possibilities, we implement such a procedure for the perfect pairing wavefunction, using a residual correlation functional that is based on the Lee–Yang–Parr functional, and present results for an elementary bond-breaking process.     

A self-consistent field scattering theory and weak asymptotic conditions

A fully self-consistent field (SCF) theory of many-particle collisions attempts to treat both the target and scattering arbitals on an equal footing, by simultaneously determining them, all self-consistently. It necessarily results in relaxation of the exact asymptotic boundary condition, because the SCF target orbitals are approximate and depend on the collision energy. Thus the original scattering problem is modified by this weak asymptotic condition (WAC) in the most fundamental was and the validity of the theory depends on multiconfiguration mixing to restore the condition. We show by extensive numerical calculations that, as more configurations are mixed, the solution converges to the correct limit. The theory is then applied to the positron-helium and electron-helium scattering systems, where the helium target functions are determined self consistently, as a part of the overall solution of the collision problem. The result shows that the weak condition is sufficient in providing physically acceptable target functions.     

A self-consistent approach to quantum field theory for extended particles

A notion of quantum space-time is introduced, physically defined as the totality of all flows of quantum test particles in free fall. In quantum space-time the classical notion of deterministic inertial frames is replaced by that of stochastic frames marked by extended particles. The same particles are used both as markers of quantum space-time points as well as natural clocks, each species of quantum test particle thus providing a standard for space-time measurements. In the considered flat-space case, the fluctuations in coordinate values with respect to stochastic frames are described by coordinate probability amplitudes related to irreducible stochastic phase space representations of the Poincaré group. Lagrangian field theory on quantum space-time is formulated. The ensuing equations of motion for interacting fields contain no singularities in their nonlinear terms, and therefore can be handled by methods borrowed from classical nonlinear analysis.Supported in part by an NSERC grant.     

A survey on HHL algorithm: From theory to application in quantum machine learning

The Harrow-Hassidim-Lloyd (HHL) algorithm is a method to solve the quantum linear system of equations that may be found at the core of various scientific applications and quantum machine learning models including the linear regression, support vector machines and recommender systems etc. After reviewing the necessary background on elementary quantum algorithms, we provide detailed account of how HHL is exploited in different quantum machine learning (QML) models, and how it provides the desired quantum speedup in all these models. At the end, we briefly discuss some of the remaining challenges ahead for HHL-based QML models and related methods.     

Nuclear level densities in self-consistent field approximation

The effect of two-body nature of the nuclear shell model potential on the recent numerical calculations of the nucleai level density has been examined. For the two most widely used single particle energy level schemes based on harmonic oscillator and Woods-Saxon potential, this effect is shown to significantly modify the excitation energy dependence of the level densisties.     

A special class of states in the self-consistent mean field approximation

In the self-consistent mean field approximation, two-level atoms penetrating an interacting medium have a special class of dressed states which, when probed with an optical field, exhibit a decreasing coupling strength to the optical field for increasing field intensities. The position of the resonance is fixed in frequency space for these states, but the linewidth varies with the intensity of the optical field.     

A theoretical model for quantum nanostructures electronic wave functions, magnetic field effects

Analytical solutions of electronic wave functions in symmetric quantum ring (QR), quantum wire (QWR) and quantum dots (QD) structures are given using a parabolic coordinates system. The solutions for low-energy states are combinations of Bessel functions. The density of states of perfect 1D QR and QWR are shown to be equivalent. The continuous evolution from a 0D QD to a perfect 1D QR can be precisely described. The sharp variation of electronic properties, related to the build up of a potential energy barrier at the early stage of the QR formation, is studied analytically. Paramagnetic and diamagnetic couplings to a magnetic field are computed for QR and QD. It is shown theoretically that magnetic field induces an oscillation of the magnetization in QR.     

Method of accurately calculating mean field operator in multi-configuration time-dependent Hartree-Fock frame

The accurate theoretical expressions of the mean field operator associated with the multi-configuration time-dependent Hartree-Fock （MCTDHF） method are presented in this paper. By using a theoretical formula, derived without approxima- tion, we can study the multi-electron correlation dynamics accurately. Some illustrative calculations are carried out to check the accuracy of the expression of the mean field operator. The results of illustrative calculations indicate the reliability of the accurate expression of the mean field operator. This theoretical calculation method for the mean field operator may be of considerable help in future studies of the correlated dynamics of many-electron systems in strong laser fields.     

A proposal for covariant renormalizable field theory of gravity

The class of covariant gravity theories which have nice ultraviolet behavior and seem to be (super)-renormalizable is proposed. The apparent breaking of Lorentz invariance occurs due to the coupling with the effective fluid which is induced by Lagrange multiplier constrained scalar field. Spatially-flat FRW cosmology for such covariant field gravity may have accelerating solutions. Renormalizable versions of more complicated modified gravity which depends on Riemann and Ricci tensor squared may be constructed in the same way.     

A parallel multigrid algorithm for percolation clusters

A new parallel cluster-finding algorithm is formulated by using multigrid relaxation methods very similar to those used for differential equation solvers. For percolation clusters, this approach drastically reduces critical slowing down relative to local or scan relaxation methods. Numerical studies of scaling properties with system size are presented in the case of the 2D percolation clusters of the Swendsen-Wang Ising dynamics running on the Connection Machine.     

Glued trees algorithm under phase damping

We study the behaviour of the glued trees algorithm described by Childs et al. in [1] under decoherence. We consider a discrete time reformulation of the continuous time quantum walk protocol and apply a phase damping channel to the coin state, investigating the effect of such a mechanism on the probability of the walker appearing on the target vertex of the graph. We pay particular attention to any potential advantage coming from the use of weak decoherence for the spreading of the walk across the glued trees graph.